Concept
A graph G = (V, E) is a non-linear data structure consisting of vertices (nodes) connected by edges, used to model networks, routing paths, and relationships.
Computer Science DSA Lab
Graph Algorithms & Network Flow Visualizer for Interactive DSA Practice
Construct custom weighted networks, trace Dijkstra shortest paths, compute Kruskal Minimum Spanning Trees, test 2-colorability, and simulate Ford-Fulkerson maximum network flow step by step. Learn the concept, operation flow, complexity, and real-world use cases through a focused OpenLabs interactive visualizer.
DSA Visualizer
Node-Edge Network & Pathfinding Engine
Dijkstra: O((V + E) log V), Kruskal: O(E log E), BFS: O(V + E), Max Flow: O(V E²)
Step 1
Build Graph
Step 2
Trace Shortest Path
Step 3
Compute Spanning Tree
Step 4
Color Vertices
Step 5
Augment Network Flow
Operation flow
Graph algorithms traverse or optimize network topologies using greedy relaxations (Dijkstra), disjoint set cycle checks (Kruskal), level-order exploration (BFS), or augmenting residual paths (Ford-Fulkerson).
Complexity
Dijkstra: O((V + E) log V), Kruskal: O(E log E), BFS: O(V + E), Max Flow: O(V E²)
Visualization
Watch each operation update the structure or algorithm state step by step.
Learn by visualizing
Understand Graph Algorithms & Network Flow through step-by-step interaction
Graph algorithms traverse or optimize network topologies using greedy relaxations (Dijkstra), disjoint set cycle checks (Kruskal), level-order exploration (BFS), or augmenting residual paths (Ford-Fulkerson). The lab makes every state change visible, helping students connect DSA theory with practical algorithm behavior.
Construct and manipulate directed and undirected weighted graphs.
Trace Dijkstra, BFS, and Bellman-Ford shortest path algorithms with live distance tables.
Compare Kruskal's (DSU) and Prim's cut-property Minimum Spanning Tree algorithms.
Solve chromatic vertex coloring and evaluate bipartite graph 2-colorability.
Simulate Ford-Fulkerson / Edmonds-Karp maximum network flow along residual capacity paths.
Where this concept is used
- GPS navigation and shortest route planning
- Network packet routing and telecom infrastructure
- Social networks and dependency graphs
- Compiler register allocation and job scheduling
- Maximum bipartite matching and pipeline flow optimization
How the interactive lab works
Open the Graph Algorithms & Network Flow lab, run the available operation controls, and watch the visual state update immediately. Use the animation to trace the operation order, compare complexity, and verify your understanding.
Curriculum Continuity
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Explore stack operations by pushing values on top, popping the latest value, and seeing last-in, first-out behavior clearly.
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Bubble Sort
Watch bubble sort compare neighboring values, swap them when needed, and move larger values toward the end of the array.
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Heap Sort
Explore heap sort by building a max heap, moving the root to the sorted region, and heapifying the remaining array.
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Insertion Sort
Watch insertion sort build a sorted prefix by picking one key at a time and inserting it into the correct position.
Graph Algorithms & Network Flow FAQs
How does Dijkstra's algorithm work?
Dijkstra uses a priority queue to greedily visit the unvisited node with the smallest tentative distance, updating/relaxing neighbor distances until the target is reached.
What is the difference between Kruskal and Prim for MST?
Kruskal sorts all edges globally and uses Union-Find (DSU) to avoid cycles. Prim starts from a seed vertex and greedily grows a single cut-property tree outward.
What is the Ford-Fulkerson method?
It computes maximum network flow by iteratively finding augmenting paths in a residual capacity graph using BFS (Edmonds-Karp) until no more capacity paths exist.
Ready to practice Graph Algorithms & Network Flow?
Launch the visualizer, trace each step, and build confidence with data structures and algorithms through hands-on learning.